bamarandy66
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If one man can rake a yard in 3 hours and another man can rake the yard in 4 hours how long would it take them to rake the yard together?
if 1 man rakes yard in 3 hrs, another rakes in 4 hrs, then
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mmm4444bot
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You did not show any work or ask any questions on your own, so I have no idea why you're stuck.
If you cannot start this exercise, or you don't know enough to ask a question, then read over the examples at the site below, and then try your exercise.
Once you know something about what you're supposed to do, then you will be able to post specific questions here. We will then be in a position to determine where to begin helping you.
CLICK HERE to see explanations and examples of "work" problems.
fasteddie65
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This is a typical algebra "work" problem.
If one man can rake a yard in 3 hours and another man can rake the yard in 4 hours how long would it take them to rake the yard together?
One way to solve these types of problems is to do the following:
If one man rakes the yard is 3 hr, then he rakes 1/3 of the yard in an hr.
If another rakes it in 4 hr, then he rakes 1/4 of the yard in an hr.
Let h = no of hr it take both of them together
(1/3)h + (1/4)h = 1
4h + 3h = 12
7h = 12
h = 12/7 or 1 5/7 hr or 1 hr 42 min 51 sec
If one man can rake a yard in 3 hours and another man can rake the yard in 4 hours how long would it take them to rake the yard together?
One way to solve these types of problems is to do the following:
If one man rakes the yard is 3 hr, then he rakes 1/3 of the yard in an hr.
If another rakes it in 4 hr, then he rakes 1/4 of the yard in an hr.
Let h = no of hr it take both of them together
(1/3)h + (1/4)h = 1
4h + 3h = 12
7h = 12
h = 12/7 or 1 5/7 hr or 1 hr 42 min 51 sec
Another way you can set it up is to note that if one man can rake a yard in 3 hours, then he rakes 1/3 a yard in 1 hour.
It is similar to eddie's approach. Just set up a little differently.
Same concept for the other raker.
\(\displaystyle \frac{1}{3}+\frac{1}{4}=\frac{1}{t}\)
Solve for t=12/7
They both rake the yard in 12/7 hours or, to be a little too precise, 1 hour 42 minutes and 51 seconds.
See how that is done. Now, you have a template to apply to future problems.
Let's toughen it up a little.
Suppose the problem said, one man can rake the yard in x hours, but the other takes twice as long as the first to rake the yard.
Together they rake it in 2 hours less than the second raker if he worked alone.
What a synapse burner, huh?.
How would we set this up?. Well, the first rakes in x hours, so we have \(\displaystyle \frac{1}{x}\) he rakes in 1 hour.
The second is twice that rate, so \(\displaystyle \frac{1}{2x}\).
Together they rake in 2 hours less than the second raker if he raked by himself..
\(\displaystyle \frac{1}{x}+\frac{1}{2x}=\frac{1}{2x-2}\)
Solve for x and we find x=3/2 hours or 1 hour and 30 minutes. That is the rate the first raker does it alone.
The second is twice that, so 3 hours by himself.
Together, they rake it in 1 hour.
Now, does this help?. You can keep this as a template for some future 'work' problems.
It is similar to eddie's approach. Just set up a little differently.
Same concept for the other raker.
\(\displaystyle \frac{1}{3}+\frac{1}{4}=\frac{1}{t}\)
Solve for t=12/7
They both rake the yard in 12/7 hours or, to be a little too precise, 1 hour 42 minutes and 51 seconds.
See how that is done. Now, you have a template to apply to future problems.
Let's toughen it up a little.
Suppose the problem said, one man can rake the yard in x hours, but the other takes twice as long as the first to rake the yard.
Together they rake it in 2 hours less than the second raker if he worked alone.
What a synapse burner, huh?.
How would we set this up?. Well, the first rakes in x hours, so we have \(\displaystyle \frac{1}{x}\) he rakes in 1 hour.
The second is twice that rate, so \(\displaystyle \frac{1}{2x}\).
Together they rake in 2 hours less than the second raker if he raked by himself..
\(\displaystyle \frac{1}{x}+\frac{1}{2x}=\frac{1}{2x-2}\)
Solve for x and we find x=3/2 hours or 1 hour and 30 minutes. That is the rate the first raker does it alone.
The second is twice that, so 3 hours by himself.
Together, they rake it in 1 hour.
Now, does this help?. You can keep this as a template for some future 'work' problems.